Skip to main content

Improvements to Bennett’s Nearest Point Algorithm for Support Vector Machines

  • Conference paper
Advances in Neural Networks – ISNN 2004 (ISNN 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3173))

Included in the following conference series:

  • 1024 Accesses

Abstract

Intuitive geometric interpretation for Support Vector Machines (SVM) provides an alternative way to implement SVM. Although Bennet’s nearest point algorithm (NPA) can deal with reduced convex hulls, it has some disadvantages. In the paper, a feasible direction explanation for NPA is proposed so that computation of kernel can be reduced greatly. Besides, the original NPA is extended to handle the arbitrary valid value of μ, therefore a better generalization performance may be obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, New York (2000)

    MATH  Google Scholar 

  2. Burges, C.J.C.: A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining and Knowledge Discovery 2(2), 1–43 (1998)

    Article  Google Scholar 

  3. Smola, A., Schölkopf, B.: A Tutorial on Support Vector Regression, NeuroCOLT Technical Report NC-TR-98-030, Royal Holloway College, University of London, UK (1998)

    Google Scholar 

  4. Bennet, K.P., Bredensteier, E.J.: Duality and Geometry in SVM Classifiers. In: Langley, P. (ed.) Proceedings of the Seventeenth International Conference on Machine Learning, pp. 57–64. Morgan Kaufmann, San Francisco (2000)

    Google Scholar 

  5. Crisp, D.J., Burges, C.J.C.: A Geometry Interpretation of μ-SVM Classifiers. In: Solla, S., Leen, T., Muller, K. (eds.) Advances in Neural Information Processing Systems (NIPS 12), pp. 244–251. MIT Press, Cambridge (2000)

    Google Scholar 

  6. Bi, J., Bennett, K.P.: Duality, Geometry, and Support Vector Regression. In: Dietterich, T., Becker, S., Ghahramani, Z. (eds.) Advances in Neural Information Processing Systems 14 (NIPS 14), pp. 593–600. MIT Press, Cambridge (2002)

    Google Scholar 

  7. Bi, J., Bennett, K.P.: A Geometric Approach to Support Vector Regression. Nerocomputing 55(1-2), 79–108 (2003)

    Article  Google Scholar 

  8. Keerthi, S.S., Shevade, S.K., Bhattcharyya, C., Murthy, K.R.K.: A Fast Iterative Nearest Point Algorithm For Support Vector Machine Classifier Design. IEEE Transactions on Neural Network 11(1), 124–136 (2000)

    Article  Google Scholar 

  9. Yang, M., Ahuja, N.: A Geometric Approach to Train Support Vector Machines. In: Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2000), pp. 1430–1437. IEEE Computer Society, Los Alamitos (2000)

    Google Scholar 

  10. Bern, M., Eppstein, D.: Optimization Over Zonotopes and Training Support Vector Machines. In: Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 2001. LNCS, vol. 2125, pp. 111–121. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Li, J., Zhang, J., Zhang, B., Lin, F. (2004). Improvements to Bennett’s Nearest Point Algorithm for Support Vector Machines. In: Yin, FL., Wang, J., Guo, C. (eds) Advances in Neural Networks – ISNN 2004. ISNN 2004. Lecture Notes in Computer Science, vol 3173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28647-9_77

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-28647-9_77

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22841-7

  • Online ISBN: 978-3-540-28647-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics